CN103441966A - Distributed MIMO frequency offset and channel estimation based on ECM under high speed - Google Patents

Abstract

The invention belongs to the technical field of wireless communication and the technical field of wireless and mobile communication, and particularly relates to a distributed MIMO frequency offset and channel estimation method based on ECM under high speed. The method comprises the steps of building a system model, carrying out initialization, calculating expectation of a complete data space, maximizing the expectation of the complete data space, updating frequency offset values, updating channel values, and carrying out iteration repeatedly until an estimation value meets requirements. According to the distributed MIMO frequency offset and channel estimation method based on the ECM under the high speed, the influences brought to the system by the high-speed moving condition are analyzed based on a united frequency offset channel estimation algorithm of a distributed MIMO system under a slow changing condition, then initialization of united frequency offset and channel estimation is carried out based on related methods, the influences brought by high speed moving are overcome by using a method based on ECM iteration, and the system is made to obtain good parameter estimation performance under a high speed moving circumstance.

Description

Distributed MIMO frequency deviation and channel estimating based on ECM under a kind of high speed

Technical field

The invention belongs to wireless and mobile communication technology field, be specifically related to distributed multiple-input and multiple-output under a kind of high-speed mobile environment (multi-input multi-output, MIMO) system combined frequency deviation and channel estimation methods.

Background technology

At following wireless communication field, the MIMO technology that is widely used in Long Term Evolution (Long Term Evolution, LTE) receives increasing the concern and research with its advantageous advantage.The MIMO Signal with Distributed Transmit Antennas networking flexibility, dual-mode antenna can be set according to specific needs and higher power system capacity can be provided, thereby becoming the principal mode of MIMO technology application.In addition, along with the develop rapidly of high-speed mobile communications, significant for the key technology research of the MIMO Signal with Distributed Transmit Antennas under high velocity environment.Because transmitting antenna and reception antenna may be distributed in different geographical position, signal has experienced different transmission channels and decline, thus MIMO Signal with Distributed Transmit Antennas distich sum of fundamental frequencies partially and channel estimating have higher requirement.Especially in high-speed mobile environment, how combining efficiently frequency deviation and the channel of estimating MIMO Signal with Distributed Transmit Antennas is one of core technology of future wireless system transmission system.

Because all transmitting antennas and the reception antenna of MIMO Signal with Distributed Transmit Antennas is distributed in different geographical position separately, signal arrives reception antenna from transmitting antenna and has experienced different large scale decline and multipath fading, so there are a plurality of different frequency deviations in it.The parameter Estimation of MIMO Signal with Distributed Transmit Antennas is actually multi-parameter and combines estimation.And based on maximum likelihood (Maximum Likelihood, ML) parameter Estimation of principle is the most practical estimation, but generally, the solution that multi-parameter based on maximum likelihood principle is estimated usually do not have closed form thereby its complexity solved higher, under the MIMO Signal with Distributed Transmit Antennas environment, this problem becomes more outstanding.In the situation that the maximum likelihood synchronized algorithm is difficult to obtain fully realization, the accurate maximal possibility estimation algorithm of suboptimum is a good selection, such as the multi-parameter algorithm for estimating based on relative theory.

Multiple Parameter Estimation Methods based on relative theory has been ignored the interference that many antennas bring, so the method has the MSE platform, and, along with the increase of signal to noise ratio, MSE can not continue to reduce.For this problem, the associating frequency deviation based on the ECM iteration and channel estimation method can effectively solve the correlation estimation method and increase the problem that produces the MSE platform with signal to noise ratio.But these algorithms all suppose that channel is to become slowly.

As from the foregoing, for MIMO Signal with Distributed Transmit Antennas, the method of employing based on relevant estimates frequency deviation and channel value as the initial value that carries out the ECM iteration, and then constantly iteration is until the frequency deviation estimated and channel value meet the demands, and this thinking can obtain performance preferably.But under high-speed mobile environment, how to adopt the ECM alternative manner to be combined frequency deviation and channel estimating to MIMO Signal with Distributed Transmit Antennas, the invention provides a kind of method that MIMO Signal with Distributed Transmit Antennas frequency deviation under high-speed mobile environment and channel are combined estimation.

Summary of the invention

Purpose of the present invention combines for the frequency deviation and the channel that solve MIMO Signal with Distributed Transmit Antennas the problem that estimation is run into when varying Channels is promoted by slow time varying channel, proposes distributed MIMO frequency deviation and channel estimating based on ECM under a kind of high speed.

The objective of the invention is to be achieved through the following technical solutions:

S1, constructing system model:

MIMO Signal with Distributed Transmit Antennas under high-speed mobile environment, have N _tn _rindividual different frequency deviation value, the signal that k reception antenna of this MIMO Signal with Distributed Transmit Antennas receives at moment t can be expressed as

$y_k\left(t\right)=\underset{l=1}{\overset{N_T}{\mathrm{\Σ}}}{h}_{k,l}\left(t\right)e^{j{w}_{k,l}t}{s}_l\left(t\right)+n_k\left(t\right),t=\mathrm{1,2},\·\·\·,N,$ Wherein, s _l(t), t=1,2 ..., the training sequence that N is l transmission antennas transmit, h _{k, l}(t) be at the t channel coefficients between l transmitting antenna and k reception antenna constantly, w _{k, l}be the frequency shift (FS) between l transmitting antenna and k reception antenna, n _k(t), t=1,2 ..., N means zero-mean, independent identically distributed multiple Gaussian noise,

Definition

y _k=[y _k(1)，y _k(2)，…，y _k(N)] ^T

$h_k={[h_{k,1},h_{k,2},\·\·\·,h_{k,N_T}]}^T$

h _k，l=[h _k，l(1)，h _k，l(2)，…，h _k，l(N)] ^T

$w_k={[w_{k,1},w_{k,2},\·\·\·,w_{k,N_T}]}^T$

N _k=[n _k(1), n _k(2) ..., n _k(N)] ^t, due to a N _t* N _rmIMO Signal with Distributed Transmit Antennas can regard equivalently N as _rthe single output of individual independently distributed many inputs (multi-input single-output, MISO) system.Therefore, for during simplifying, we can consider the DISTRIBUTED MIS O system of 2 * 1 equivalently.So, at the reception signal of moment t, can be expressed as

$y\left(t\right)=\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(t\right)e^{j{w}_{l}t}{s}_l\left(t\right)+n\left(t\right),t=\mathrm{1,2},\·\·\·,N,$

Definition

w=[w ₁ w ₂] ^T

$\mathrm{\Φ}\left(w_1\right)=\mathrm{diag}\left(\begin{array}{c}\end{array}\left[\begin{array}{cccc}{e}^{j{w}_1}& e^{j2w_1}& ...& e^{\mathrm{jN}{w}_1}\end{array}\right]\right)$

$\mathrm{\Φ}\left(w_2\right)=\mathrm{diag}\left(\begin{array}{}\end{array}\begin{array}{c}\end{array}\left[\begin{array}{cccc}{e}^{j{w}_2}& e^{j2w_2}& ...& e^{\mathrm{jN}{w}_2}\end{array}\right]\right),$

h ₁=diag([h ₁(1) h ₁(2) … h ₁(N)])

h ₂=diag([h ₂(1) h ₂(2) … h ₂(N)])

If the sequence of first transmission antennas transmit is s ₁=[s ₁(1) 0 s ₁(3) ... s ₁(N-1) 0] ^t, the sequence of second transmission antennas transmit is s ₂=[0 s ₂(2) 0 ... 0 s ₂(N)] ^t, can make to received signal as down conversion,

$\left[\begin{array}{c}\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(1\right)e^{j{w}_l}{s}_l\left(1\right)+n\left(1\right)\\ \underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_1\left(2\right)e^{{j2w}_l}{s}_l\left(2\right)+n\left(2\right)\\ \·\\ \·\\ \·\\ \underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(N\right)e^{{\mathrm{jNw}}_l}{s}_l\left(N\right)+n\left(N\right)\end{array}\right]=h_1\mathrm{\Φ}\left(w_1\right)s_1+h_2\mathrm{\Φ}\left(w_2\right)s_2+n,$

$=\left[\begin{array}{c}{h}_1\left(1\right)e^{j{w}_1}{s}_1\left(1\right)\\ h_2\left(2\right)e^{{j2w}_2}{s}_2\left(2\right)\\ h_1\left(3\right)e^{j3w_1}{s}_1\left(3\right)\\ \·\\ \·\\ \·\\ h_1(N-1)e^{{j(N-1)w}_1}{s}_1(N-1)\\ h_2\left(N\right)e^{\mathrm{jN}{w}_2}{s}_2\left(N\right)\end{array}\right]+n={\mathrm{\Φ}}_{s}h+n$

Wherein, ${\mathrm{\Φ}}_s=\mathrm{diag}\left(\begin{array}{c}\end{array}\left[\begin{array}{cccccc}{s}_1\left(1\right)e^{j{w}_1}& s_2\left(2\right)e^{j2w_2}& s_1\left(3\right)e^{j3w_1}& ...& s_1(N-1)e^{j(N-1)w_2}& s_2\left(N\right)e^{\mathrm{jN}{w}_2}\end{array}\right]\right);$ H=[h ₁(1) h ₂(2) h ₁(3) ... h ₁(N-1) h ₂(N)] ^t,, the reception signal indication of t is y=Φ constantly _sh+n, by minimizing target function

frequency deviation skew and channel h are carried out to the ML estimation, when in the situation that frequency shift (FS) is certain, can first try to achieve h ₀=(Φ _s ^hΦ _s) ^-1Φ _s ^hy and then can obtain

S2, initialization:

Receiving terminal will receive signal and the training sequence of l transmitting antenna will be made to relevant treatment, obtain

wherein, P is correlation length, remakes the first difference relevant treatment with the training sequence of l transmitting antenna to received signal, and the difference distance is i, obtains especially, when the difference distance is made as 1, have

the frequency deviation between l transmitting antenna and first reception antenna is offset w _{l, 1}the estimation expression formula be

wherein, T is symbol period, and the frequency deviation initial value that can obtain between transmitting antenna 1 and reception antenna is

and between transmitting antenna 2 and reception antenna, inclined to one side initial value is

and then can obtain the channel initial value and be

The expectation in S3, calculating complete data space:

The training sequence that we define l transmission antennas transmit is s _l=[s _l(1), s _l(2) ..., s _l(N)] ^t, define l transmission antennas transmit the form of frequency deviation be

, receiving signal indication is

n=[n (1), n (2) ..., n (N)] ^tand n～CN (0, σ ²i _n); h _l=[h _l(1), h _l(2) ..., h _l(N)], l=1,2.Treat that estimated parameter is

θ wherein _l=[w _l, h _l] ^tfrequency deviation and channel between corresponding l transmitting antenna and reception signal, receiving signal y is non-complete data space, however non-complete data space can, by the complete data spatial characterization, therefore define complete data space z=[z ₁, z ₂] ^t, wherein,

the relation of complete data space z and non-complete data space y can be expressed as $\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{z}_l=y,$

Total noise n is divided into to two parts, that is,

wherein, n _lbe the Gaussian noise of independent same distribution, zero-mean, variance is β _lσ ²i _n,

Suppose β _lequate, i.e. β _l=1/N _t=1/2, the m time iteration ask complete data space expectation as follows:

The log-likelihood function in complete data space can be expressed as

due to noise n _lto add up independently, so z is for the probability-distribution function (probability density function, PDF) of θ

can obtain

wherein, ${\hat{z}}_l^{\left[m\right]}=E\left\{z_l\right|y,{\widehat{\mathrm{\θ}}}^{\left[m\right]}\},$ for the expectation of complete data space, due to z _lobey Joint Gaussian distribution with y, wherein,

The expectation in S4, maximization complete data space:

Expectation to S3 gained complete data space

maximized, obtained the maximization renewal value of solve for parameter θ

S5, renewal frequency deviation value:

According to S4

to solve for parameter, θ is minimized renewal, obtains minimizing the renewal value

exist 2 sons to minimize renewal process,

When the antithetical phrase minimization process is upgraded, ECM algorithm handle

renewal process carry out in two steps, upgrade respectively frequency deviation and channel, under constant condition, at first frequency deviation is minimized to renewal at fixed channel

place carries out the second order Taylor series expansion and can obtain $e^{j{w}_{l}t}\≈e^{j{\hat{w}}_l^{\left[m\right]}t}+(w_l-{\hat{w}}_l^{\left[m\right]})\left(\mathrm{jt}\right)e^{j{\hat{w}}_l^{\left[m\right]}t}+\frac{1}{2}{(w_l-{\hat{w}}_l^{\left[m\right]})}^2{\left(\mathrm{jt}\right)}^2{e}^{j{\hat{w}}_l^{\left[m\right]}t},$ Emulation shows

(40) formula convex function always, and to w _ldifferentiating and making it is 0, solves frequency deviation renewal value

for

S6, renewal channel value:

Fix its value constant after frequency deviation is upgraded, then channel coefficients is upgraded, obtain channel coefficients renewal value

for ${\hat{h}}_l^{[m+1]}\left(t\right)=\arg \underset{h_l\left(t\right)}{\min }{|{\hat{z}}_l^{\left[m\right]}\left(t\right)-s_l\left(t\right)e^{j{\hat{w}}_l^{[m+1]}t}{h}_l\left(t\right)|}^2,t=\mathrm{1,2},\·\·\·,N,$

${\hat{h}}_l^{[m+1]}\left(t\right)=\frac{1}{{\left|s_l\left(t\right)\right|}^2}*\frac{{\hat{z}}_l^{\left[m\right]}\left(t\right)s_l^{*}\left(t\right)}{e^{j{\hat{w}}_l^{[m+1]}t}},t=\mathrm{1,2},...,N,$ Wherein,

(t) be l transmitting antenna obtaining of the m+1 time iteration and the value of channel when moment t between reception antenna, so far

this renewal of m+1 completes;

S7, iteration know that estimated value meets the demands:

By the S6 gained

as initial value traversal S5 and S6, carry out again iteration and upgrade, know that iteration renewal value meets the demands.

Further, the described β of S3 _lmeet

β _l>0.

Further, the described C of S3 ₁and C ₂two constants that are independent of θ.

The invention has the beneficial effects as follows: the associating frequency deviation channel estimation method of the MIMO Signal with Distributed Transmit Antennas from change condition slowly, analyze the impact that high-speed mobile condition brings to system, then adopt the method based on relevant combined the initialization of frequency deviation and channel estimating and then adopt the method based on the ECM iteration to overcome the impact that high-speed mobile is brought, make system obtain parameter Estimation performance preferably under high-speed mobile environment.

The accompanying drawing explanation

Fig. 1 is the present invention's MIMO Signal with Distributed Transmit Antennas schematic diagram used.

Fig. 2 is specific algorithm steps flow chart schematic diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described:

S1: constructing system model.

We consider a MIMO Signal with Distributed Transmit Antennas under high-speed mobile environment, have N _tindividual transmitting antenna and N _rindividual reception antenna.A different frequency deviation value is arranged between every pair of dual-mode antenna, so the system that the present invention considers has N _tn _rindividual different frequency deviation value.The signal that k reception antenna of this system receives at moment t can be expressed as

$y_k\left(t\right)\underset{l=1}{\overset{N_T}{\mathrm{\Σ}}}{h}_{k,l}\left(t\right)e^{j{w}_{k,l}t}{s}_l\left(t\right)+n_k\left(t\right),t=\mathrm{1,2},...,N---\left(1\right)$

Wherein, S _l(t), t=1,2 ..., the training sequence that N is l transmission antennas transmit; h _{k, l}(t) be at the t channel coefficients between l transmitting antenna and k reception antenna constantly; w _k, _lit is the frequency shift (FS) between l transmitting antenna and k reception antenna; n _k(t), t=1,2 ..., V means zero-mean, independent identically distributed multiple Gaussian noise.

Definition

y _k=[y _k(1)，y _k(2)，…，y _k(N)] ^T (2)

$h_k={[h_{k,1},h_{k,2},...,h_{k,H_T}]}^T---\left(3\right)$

h _k,l=[h _k,l(1)，h _k,l(2)，…，h _k,l(N)] ^T (4)

$w_k={[w_{k,1},w_{k,2},...,w_{k,N_T}]}^T---\left(5\right)$

n _k=[n _k(1)，n _k(2)，…，n _k(N)] ^T (6)

Due to a N _t* N _rmIMO Signal with Distributed Transmit Antennas can regard equivalently N as _rthe single output of individual independently distributed many inputs (multi-input single-output, MISO) system.Therefore, for during simplifying, we can consider the DISTRIBUTED MIS O system of 2 * 1 equivalently.So, at the reception signal of moment t, can be expressed as

$y\left(t\right)=\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(t\right)e^{j{w}_{l}t}{s}_l\left(t\right)+n\left(t\right),t=\mathrm{1,2},...,N---\left(7\right)$

We define

w=[w ₁w ₂] ^T (8)

$\mathrm{\Φ}\left(w_1\right)=\mathrm{diag}\left(\left[\begin{array}{cccc}{e}^{{\mathrm{jw}}_1}& e^{{j2w}_1}& ...& e^{{\mathrm{jNw}}_1}\end{array}\right]\right)---\left(9\right)$

$\mathrm{\Φ}\left(w_2\right)=\mathrm{diag}\left(\right[e^{j{w}_2}{e}^{j2w_2}...e^{\mathrm{jN}{w}_2}\left]\right)---\left(10\right)$

h ₁=diag([h ₁(1)h ₁(2)…h ₁(N)]) (11)

h ₂=diag([h ₂(1)h ₂(2)…h ₂(N)]) (12)

We suppose that the sequence of first transmission antennas transmit is s ₁=[s ₁(1) 0 s ₁(3) ... s ₁(N-1) 0] ^t; The sequence of second transmission antennas transmit is s ₂=[0 s ₂(2) 0 ... 0 s ₂(N)] ^t.So, receiving signal can do as down conversion

$y=\left[\begin{array}{c}\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(1\right)e^{j{w}_l}{s}_l\left(1\right)+n\left(1\right)\\ \underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(2\right)e^{j2w_l}{s}_l\left(2\right)+n\left(2\right)\\ .\\ .\\ .\\ \underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(N\right)e^{\mathrm{jN}{w}_l}{s}_l\left(N\right)+n\left(N\right)\end{array}\right]=h_1\mathrm{\Φ}\left(w_1\right)s_1+h_2\mathrm{\Φ}\left(w_2\right)s_2+n$ (13)

$=\left[\begin{array}{c}{h}_1\left(1\right)e^{j{w}_1}{s}_1\left(1\right)\\ h_2\left(2\right)e^{j2w_2}{s}_2\left(2\right)\\ h_1\left(3\right)e^{j3w_1}{s}_1\left(3\right)\\ .\\ .\\ .\\ h_1(N-1)e^{j(N-1)w_1}{s}_1(N-1)\\ h_2\left(N\right)e^{\mathrm{jN}{w}_2}{s}_2\left(N\right)\end{array}\right]+n={\mathrm{\Φ}}_{s}h+n$

Wherein, ${\mathrm{\Φ}}_s=\mathrm{diag}\left(\right[s_1\left(1\right)e^{j{w}_1}{s}_2\left(2\right)e^{j2w_2}{s}_1\left(3\right)e^{j3w_1}...s_1(N-1)e^{j{(N-1)w}_2}{s}_2\left(N\right)e^{\mathrm{jN}{w}_2}\left]\right);$

h=[h ₁(1) h ₂(2) h ₁(3) … h ₁(N-1) h ₂(N)] ^T.

Therefore, formula (7) can be expressed as

y=Φ _sh+n (14)

The ML of frequency deviation skew and channel estimates to realize by minimizing target function (15) formula

A=‖y-Φ _sh‖ ² (15)

When in the situation that frequency shift (FS) is certain, can in the hope of

h ₀=(Φ _s ^HΦ _s) ^-1Φ _s ^Hy (16)

(16) formula is brought into to (15) formula, and the multifrequency of MIMO Signal with Distributed Transmit Antennas is estimated to become (17) formula is carried out to multi-dimensional optimization partially, has

$w=\arg \underset{w}{\max }{y}^H{\mathrm{\Φ}}_s{\left({\mathrm{\Φ}}_s^H{\mathrm{\Φ}}_s\right)}^{-1}{\mathrm{\Φ}}_s^{H}y---\left(17\right)$

S2: initialization.

Receiving terminal will receive signal and the training sequence of l transmitting antenna will be made to relevant treatment, obtain

$R_{s_l}\left(k\right)=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{s}_l(\mathrm{kP}+p)y(\mathrm{kP}+p)---\left(18\right)$

Wherein, P is correlation length.

Remake first difference relevant, the difference distance is i, obtains

$C_l\left(i\right)=E\left\{R_{s_l}\left(k\right){\left(R_{s_l}(k-i)\right)}^{*}\right\},l=\mathrm{1,2}$

(19)

Especially, when the difference distance is made as 1, have

So, the skew of the frequency deviation between l transmitting antenna and first reception antenna w _{l, 1}the estimation expression formula be

${\hat{w}}_{l,1}=\frac{1}{2\mathrm{\πPT}}\mathrm{ary}\left({\hat{C}}_l\left(1\right)\right)---\left(21\right)$

Wherein, T is symbol period.

So, can obtain two transmitting antennas 1 and 2 and reception antenna between the frequency deviation initial value be respectively

${\hat{w}}_1=\frac{1}{2\mathrm{\πPT}}\arg \left({\hat{C}}_1\left(1\right)\right)---\left(22\right)$

${\hat{w}}_2=\frac{1}{2\mathrm{\πPT}}\arg \left({\hat{C}}_2\left(1\right)\right)---\left(23\right)$

Above-mentioned two frequency deviation initial values are obtained to the channel initial value and be as the known formula (16) of bringing into

$\hat{h}={\left({{\mathrm{\Φ}}_s}^H{\mathrm{\Φ}}_s\right)}^{-1}{{\mathrm{\Φ}}_s}^{H}y---\left(24\right)$

Using top frequency deviation and channel initial value as the initial value that carries out the ECM iteration.

S3: the expectation of calculating the complete data space.

Particularly, we define the training sequence of l transmission antennas transmit and the form of frequency deviation is

s _l=[s _l(1)，S _l(2)，…，S _l(N)] ^T (25)

$W_l=[e^{j{\mathrm{\ω}}_l},e^{j2{\mathrm{\ω}}_l},...,e^{\mathrm{jN}{\mathrm{\ω}}_l}]---\left(26\right)$

So receiving signal can be expressed as

Wherein, n=[n (1), n (2) ..., n (N)] ^tand n～CN (0, σ ²i _n); h _l=[h _l(1), h _l(2) ..., h _l(N)], l=l, 2.Treat that estimated parameter is

, θ wherein _l=[w _l, h _l] ^tfrequency deviation and channel between corresponding l transmitting antenna and reception signal.Receiving signal y is non-complete data space, yet non-complete data space can, by the complete data spatial characterization, therefore define complete data space z=[z ₁, z ₂] ^t, wherein

Therefore the relation of complete data space z and non-complete data space y can be expressed as

$\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{Z}_l=y$

(29)

Total noise n is divided into to two parts,

$\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{n}_l=n---\left(30\right)$

Wherein, n _lbe the Gaussian noise of independent same distribution, zero-mean, variance is β _lσ ²i _n.Wherein, β _lmeet following condition

$\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{\mathrm{\β}}_l=1,{\mathrm{\β}}_l>0$

(31)

We suppose β _lequate, i.e. β _l=1/N _t=1/2.

The m time iteration ask complete data space expectation as follows:

The log-likelihood function in complete data space can be expressed as

$Q\left(\mathrm{\θ}\right|{\widehat{\mathrm{\θ}}}^{\left[m\right]})\stackrel{\mathrm{\Δ}}{=}E\left\{\log f\left(z\right|\mathrm{\θ})\right|y,{\widehat{\mathrm{\θ}}}^{\left[m\right]}\}---\left(32\right)$

Due to noise n _lto add up independently, so z is for the probability-distribution function (probability density function, PDF) of θ

Formula (33) is brought into to formula (32) can be obtained,

(34)

Wherein

${\hat{z}}_l^{\left[m\right]}=E\left\{z_l\right|y,{\widehat{\mathrm{\θ}}}^{\left[m\right]}\}$ (35)

In addition, C ₁and C ₂two constants that are independent of θ.

Because z _lobey Joint Gaussian distribution with y, by (29) Shi Ke get

Wherein

${\hat{W}}_v^{\left[m\right]}={[e^{j{\hat{w}}_v^{\left[m\right]},e^{j2{\hat{w}}_v^{\left[m\right]}},}...,e^{\mathrm{jN}{\hat{w}}_v^{\left[m\right]}}]}^T---\left(37\right)$

Formula (34) is the expectation in complete data space.

S4: maximize the expectation in complete data space.

The renewal value of solve for parameter θ

can be expressed as

(38)

As can be seen from the above equation, it minimizes renewal process can be divided into 2 (is v _t) height minimizes renewal process,

(39)

S5: upgrade frequency deviation value.

When the antithetical phrase minimization process is upgraded, ECM algorithm handle

renewal process carry out in two steps, upgrade respectively frequency deviation and channel.

Under constant condition, at first frequency deviation is minimized to renewal at fixed channel

place carries out the second order Taylor series expansion and can obtain

$e^{j{w}_{l}t}\≈e^{j{\hat{w}}_l^{\left[m\right]}t}+(w_l-{\hat{w}}_l^{\left[m\right]}){\left(\mathrm{jt}\right)}^{e^{j{\hat{w}}_l^{\left[m\right]}t}}+\frac{1}{2}{(w_l-{\hat{w}}_l^{\left[m\right]})}^2{\left(\mathrm{jt}\right)}^2{e}^{j{\hat{w}}_l^{\left[m\right]}t}---\left(41\right)$

Emulation shows always convex function of (40) formula, therefore (41) formula is brought into to (42) formula, and to w _ldifferentiating and making it is 0, solves frequency deviation renewal value

for

S6: upgrade channel value.

Fix its value constant after frequency deviation is upgraded, then channel coefficients is upgraded, obtain channel coefficients renewal value

for

${\hat{h}}_l^{[m+1]}\left(t\right)=\arg \underset{h_l\left(t\right)}{\min }{|{\hat{z}}_l^{\left[m\right]}\left(t\right)-s_l\left(t\right)e^{j{\hat{w}}_l^{[m+1]}t}{h}_l\left(t\right)|}^{2}t=\mathrm{1,2}\·\·\·,N---\left(43\right)$

The abbreviation above formula can obtain

${\hat{h}}_l^{[m+1]}\left(t\right)=\frac{1}{{\left|s_l\left(t\right)\right|}^2}*\frac{{\hat{z}}_l^{\left[m\right]}\left(t\right)s_l^{*}\left(t\right)}{e^{j{\hat{w}}_l^{[m+1]}t}}t=\mathrm{1,2},\·\·\·N---\left(44\right)$

Wherein

be l transmitting antenna obtaining of the m+1 time iteration and the value of channel when moment t between reception antenna.

So far, ${\widehat{\mathrm{\θ}}}_l^{[m+1]}={[{\hat{w}}_l^{[m+1]},{\hat{h}}_l^{[m+1]}]}^T,$ This renewal of m+1 completes.

S7: iteration until estimated value meet the demands.

The latest update value

carry out again the iteration renewal as initial value substitution step 5 again and step 6, until iteration renewal value meets the demands.

Claims (3)

1. distributed MIMO frequency deviation and the channel estimating based on ECM under a high speed, it is characterized in that: its step is as described below:

S1, constructing system model:

MIMO Signal with Distributed Transmit Antennas under high-speed mobile environment, have N _tn _rindividual different frequency deviation value, the signal that k reception antenna of this MIMO Signal with Distributed Transmit Antennas receives at moment t can be expressed as

, wherein, s _l(t), t=1,2 ..., the training sequence that N is l transmission antennas transmit, h _{k, l}(t) be at the t channel coefficients between l transmitting antenna and k reception antenna constantly, w _{k, l}be the frequency shift (FS) between l transmitting antenna and k reception antenna, n _k(t), t=1,2 ..., N means zero-mean, independent identically distributed multiple Gaussian noise,

Definition

y _k=[y _k(1)，y _k(2)，…，y _k(N)] ^T

$h_k={[h_{k,1},k_{k,2},\·\·\·,h_{{k,N}_T}]}^T$

h _k，l=[h _k，l(1)，h _k，l(2)，…，h _k，l(N)] ^T

$w_k={[w_{k,1},w_{k,2},\·\·\·,w_{{k,N}_T}]}^T$

N _k=[n _k(1), n _k(2) ..., n _k(N)] ^t, due to a N _t* N _rmIMO Signal with Distributed Transmit Antennas can regard equivalently N as _rthe single output of individual independently distributed many inputs (multi-input single-output, MISO) system.Therefore, for during simplifying, we can consider the DISTRIBUTED MIS O system of 2 * 1 equivalently, so, at the reception signal of moment t, can be expressed as

$y\left(t\right)=\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(t\right)e^{j{w}_{l}t}{s}_l\left(t\right)+n\left(t\right),t=\mathrm{1,2},\·\·\·,N,$

Definition

w=[w ₁ w ₂] ^T

$\mathrm{\Φ}\left(w_1\right)=\mathrm{diag}\left(\begin{array}{c}\end{array}\left[\begin{array}{cccc}{e}^{j{w}_1}& e^{j2w_1}& \·\·\·& e^{\mathrm{jN}{w}_1}\end{array}\right]\right)$

$\mathrm{\Φ}\left(w_2\right)=\mathrm{diag}\left(\begin{array}{c}\end{array}\left[\begin{array}{cccc}{e}^{j{w}_2}& e^{j2w_2}& \·\·\·& e^{\mathrm{jN}{w}_2}\end{array}\right]\right)$

h ₁=diag([h ₁(1) h ₁(2)…h ₁(N)])

h ₂=diag([h ₂(1) h ₂(2)…h ₂(N)])，

If the sequence of first transmission antennas transmit is s ₁=[s ₁(1) 0 s ₁(3) ... s ₁(N-1) 0] ^t, the sequence of second transmission antennas transmit is s ₂=[0 s ₂(2) 0 ... 0 s ₂(N)] ^t, can make to received signal as down conversion,

$y=\left[\begin{array}{c}\underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(1\right)e^{j{w}_l}{s}_l\left(1\right)+n\left(1\right)\\ \underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(2\right)e^{j2w_l}{s}_l\left(2\right)+n\left(2\right)\\ \·\\ \·\\ \·\\ \underset{l=1}{\overset{2}{\mathrm{\Σ}}}{h}_l\left(N\right)e^{\mathrm{jN}{w}_l}{s}_l\left(N\right)+n\left(N\right)\end{array}\right]=h_1\mathrm{\Φ}\left(w_1\right)s_1+h_2\mathrm{\Φ}\left(w_2\right)s_2+n$

$=\left[\begin{array}{c}{h}_1\left(1\right)e^{j{w}_1}{s}_1\left(1\right)\\ h_2\left(2\right)e^{j2w_2}{s}_2\left(2\right)\\ h_1\left(3\right)e^{j3w_1}{s}_1\left(3\right)\\ \·\\ \·\\ \·\\ h_1(N-1)e^{j(N-1)w_1}{s}_1(N-1)\\ h_2\left(N\right)e^{\mathrm{jN}{w}_2}{s}_2\left(N\right)\end{array}\right]+n={\mathrm{\Φ}}_{s}h+n,$

Wherein, ${\mathrm{\Φ}}_s=\mathrm{diag}\left(\begin{array}{}\end{array}\left[\begin{array}{cccccc}{s}_1\left(1\right)e^{j{w}_1}& s_2\left(2\right)e^{j2w_2}& s_1\left(3\right)e^{j3w_1}& \·\·\·& s_1(N-1)e^{j(N-1)w_2}& s_2\left(N\right)e^{\mathrm{jN}{w}_2}\end{array}\right]\right),$

H=[h ₁(1) h ₂(2) h ₁(3) ... h ₁(N-1) h ₂(N)] ^t,, the reception signal indication of t is y=Φ constantly _sh+n, by minimize target function Λ=|| y-Φ _sh|| ²frequency deviation skew and channel h are carried out to the ML estimation, when in the situation that frequency shift (FS) is certain, can first try to achieve h ₀=(Φ _s ^hΦ _s) ^-1Φ _s ^hy and then can obtain

S2, initialization:

Receiving terminal will receive signal and the training sequence of l transmitting antenna will be made to relevant treatment, obtain

, wherein, P is correlation length, remakes the first difference relevant treatment with the training sequence of l transmitting antenna to received signal, the difference distance is i, obtains

especially, when the difference distance is made as 1, have

, the frequency deviation between l transmitting antenna and first reception antenna is offset w _{l, 1}the estimation expression formula be

wherein, T is symbol period, and the frequency deviation initial value that can obtain between transmitting antenna 1 and reception antenna is

and between transmitting antenna 2 and reception antenna, inclined to one side initial value is

and then can obtain the channel initial value and be $\hat{h}={\left({{\mathrm{\Φ}}_s}^H{\mathrm{\Φ}}_s\right)}^{-1}{{\mathrm{\Φ}}_s}^{H}y;$

The expectation in S3, calculating complete data space:

The training sequence that defines l transmission antennas transmit is s _l=[s _l(1), s _l(2) ..., s _l(N)] ^t, define l transmission antennas transmit the form of frequency deviation be

, receiving signal indication is

, n=[n (1), n (2) ..., n (N)] ^tand n～CN (0, σ ²i _n); h _l=[h _l(1), h _l(2) ..., h _l(N)], l=1,2, treat that estimated parameter is

, θ wherein _l=[w _l, h _l] ^tfrequency deviation and channel between corresponding l transmitting antenna and reception signal, receiving signal y is non-complete data space, however non-complete data space can, by the complete data spatial characterization, therefore define complete data space z=[z ₁, z ₂] ^t, wherein,

, the relation of complete data space z and non-complete data space y can be expressed as

, total noise n is divided into to two parts, that is,

, wherein, n _lbe the Gaussian noise of independent same distribution, zero-mean, variance is β _lσ ²i _n, suppose β _lequate, i.e. β _l=1/N _t=1/2, the m time iteration ask complete data space expectation as follows, the log-likelihood function in complete data space can be expressed as

due to noise n _lto add up independently, so z is for the probability-distribution function (probability density function, PDF) of θ

, can obtain

, wherein, ${\hat{z}}_l^{\left[m\right]}=E\left\{z_l\right|y,{\widehat{\mathrm{\θ}}}^{\left[m\right]}\},Q\left(\mathrm{\θ}\right|{\widehat{\mathrm{\θ}}}^{\left[m\right]})$ For the expectation of complete data space, due to z _lobey Joint Gaussian distribution with y, wherein,

The expectation in S4, maximization complete data space:

Expectation to S3 gained complete data space maximized, obtained the maximization renewal value of solve for parameter θ

S5, renewal frequency deviation value:

According to S4

to solve for parameter, θ is minimized renewal, obtains minimizing the renewal value

,, exist 2 sons to minimize renewal process, when the antithetical phrase minimization process is upgraded, ECM algorithm handle renewal process carry out in two steps, upgrade respectively frequency deviation and channel, under constant condition, at first frequency deviation is minimized to renewal at fixed channel

,

place carries out the second order Taylor series expansion and can obtain $e^{j{w}_{l}t}\≈e^{j{\hat{w}}_l^{{\left[m\right]}_t}}+(w_l-{\hat{w}}_l^{\left[m\right]})\left(\mathrm{jt}\right)e^{j{\hat{w}}_l^{{\left[m\right]}_t}}+\frac{1}{2}{(w_l-{\hat{w}}_l^{\left[m\right]})}^2{\left(\mathrm{jt}\right)}^2{e}^{j{\hat{w}}_l^{{\left[m\right]}_t}},$ Emulation shows (40) formula convex function always, and to w _ldifferentiating and making it is 0, solves frequency deviation renewal value

for

S6, renewal channel value:

Fix its value constant after frequency deviation is upgraded, then channel coefficients is upgraded, obtain channel coefficients renewal value

for ${\hat{h}}_l^{[m+1]}\left(t\right)=\arg \underset{h_l\left(t\right)}{\min }{|{\hat{z}}_l^{\left[m\right]}\left(t\right)-s_l\left(t\right)e^{j{\hat{w}}_l^{{[m+1]}_t}}{h}_l\left(t\right)|}^{2}t=\mathrm{1,2},\·\·\·,N,$ ${\hat{h}}_l^{[m+1]}\left(t\right)\frac{1}{{\left|s_l\left(t\right)\right|}^2}*\frac{{\hat{z}}_l^{\left[m\right]}\left(t\right)s_l^{*}\left(t\right)}{e^{j{\hat{w}}_l^{{[m+1]}_t}}}t=\mathrm{1,2},\·\·\·,N,$ Wherein,

be l transmitting antenna obtaining of the m+1 time iteration and the value of channel when moment t between reception antenna, so far

this renewal of m+1 completes;

S7, iteration know that estimated value meets the demands:

By the S6 gained

as initial value traversal S5 and S6, carry out again iteration and upgrade, know that iteration renewal value meets the demands.

2. distributed MIMO frequency deviation and the channel estimating based on ECM under a kind of high speed according to claim 1, is characterized in that: the described β of S3 _lmeet

3. distributed MIMO frequency deviation and the channel estimating based on ECM under a kind of high speed according to claim 1, is characterized in that: the described C of S3 ₁and C ₂two constants that are independent of θ.

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